Try clicking on it. It'll say it can't find it, but I think it'll also remove it from the list. (I haven't had CS6 open for a very long time, so I don't recall.
In the future, questions like this should go in the regular After Effects forum rather than After Effects Resources. The other one has a lot more traffic, plus is about support for AE whereas this one is more about resources for it. I'll get a moderator to move your post.
Not that I know of, but if you click on a recent project that no longer exists, what do you think will happen? Nothin'.
Thank you for your help.
Background: I must have been using an old tutorial from Lynda HOT Projects that needed to be converted where I found the aep projects. These were not in the Adobe folder. Hence AE CS6 could not find them. I moved them back to the Adobe folder. This was my problem for not changing the Save folder after using HOT Projects. I do not know if this would have influenced my feedback to your question.
After clicking the projects in the AE6 Open recent projects list, the following dialog noted they could not be found. Upon exit then reopening AE CS6, the projects were still there showing the link to HOT Projects.